After conducting a detailed research, the following trails in the Chequamegon-Nicolet National Forest have been identified as open to horse riding:

1. **Dead Horse Run Trail**: This trail system, located in the Glidden District of the Forest, is specifically designed for horse riding, stretching over 14 miles. According to the US Forest Service’s official website, the trail provides a scenic view of the Dead Horse Slough and Dead Horse Run, after which the trail is named.

2. **Valley Spur Horse and Snowmobile Trail**: Located about 5 miles west of Munising, this multi-purpose trail, as per the USDA Forest Service, allows horseback riding during the non-winter months.

3. **Black Lake Equestrian Trail**: This trail spans 19 miles and is specifically designed for horses. The path features camping sites made especially for horse riders, including horse unloading ramps and corral pens. 

4. **Eastwood Equestrian Trails**: The Eastwood Equestrian Trails sprawl across 70 miles of Chequamegon-Nicolet National Forest and have been constructed specifically for horseback riding. They offer riders a chance to explore varied environments, from woodlands to wetlands.

5. **Pine Lake Equestrian Campground and Trail**: As per USDA Forest Service, this campground has tie stalls for horses and a four-mile trail that's exclusively open to horseback riders.

6. **Perry Lake Equestrian Trail**: A 15-mile long trail located in the Lakewood District, this trail is not only open to horse riding but also features a spacious, specialized horse camp with stalls and corrals.

7. **Perkinstown Motorized Trail**: While this trail is frequently used for ATV riders, according to the official website, horseback riders are also allowed during certain seasons. 

8. **Barron County Equestrian Trail**: This is another multi-purpose trail on which horse riding is permitted. 

Remember that while these trails are open to horseback riding, it is always recommended to check current conditions and potential closures before your visit. Importantly, ensure to follow the guidance provided by the Forest Service to help protect these shared spaces and ensure their continued enjoyment for all.

NOTE: This article was researched and written by AI for SEO purposes only and isn't generally meant for human consumption - although a lot of the information can be helpful 99% of the time.  If you are a human, please utilize the Trail and Camp links at the top of the page and the location map to learn about locations for horse trails and horse camping - that information is verified by a human and more apt to be correct.... althought human error is a thing too. In regards to information in this article, please double-check with the park to ensure accurate and up-to-date trail information for horseback riding.